Knitting a flat circle - the math?

I want to knit a flat circle (about 10" across) and not use short rows. I've
looked at a couple of dishcloth and doily patterns and am trying to figure
out the math used to get it flat.

All the ones I've seen have you start in the middle with a few stitches on
DPN. I'd rather start on the outside using a circular and then graduate to
DPNs as you get closer to the center. (I know, I just HAVE to be difficult!)
I just think it would be easier.

I know you must decrease with each round, but by how much? If I start with,
say 100 sts on a circular, is there a formula I should use to know when to
decrease - Knit 2 together every X stitches?

Any insight appreciated!
Abi

On Thu, 10 Mar 2005 13:25:51 -0500, Gallagher babbled something about:
mercilessly snipped

I know you must decrease with each round, but by how much? If I start with,
say 100 sts on a circular, is there a formula I should use to know when to
decrease - Knit 2 together every X stitches?
Abi

I just *know* that either Sonya or Wooly are going to beat me to the
answer while I do the math.... but if they don't... I'll get back to
ya, Abi! (Personally, *I'd* start in the middle....)

Hugs,
Noreen


--
~ change n e t to c o m to email me ~
\or\
~ Strip "tease" to email me ~

You'll end up on DPNs either way...

Working from the outside in you should treat it like the crown of a
tam, which, IIRC, uses double decreases (s2kw, k1, p2sso) every other
round at 8 points.

Its easier to work from the inside to the outer edge, imo.

On Thu, 10 Mar 2005 13:25:51 -0500, "Gallagher"
spewed forth :

I want to knit a flat circle (about 10" across) and not use short rows. I've
looked at a couple of dishcloth and doily patterns and am trying to figure
out the math used to get it flat.

All the ones I've seen have you start in the middle with a few stitches on
DPN. I'd rather start on the outside using a circular and then graduate to
DPNs as you get closer to the center. (I know, I just HAVE to be difficult!)
I just think it would be easier.

I know you must decrease with each round, but by how much? If I start with,
say 100 sts on a circular, is there a formula I should use to know when to
decrease - Knit 2 together every X stitches?

Any insight appreciated!
Abi

In article , "Gallagher"
wrote:

I want to knit a flat circle (about 10" across) and not use short rows. I've
looked at a couple of dishcloth and doily patterns and am trying to figure
out the math used to get it flat.

All the ones I've seen have you start in the middle with a few stitches on
DPN. I'd rather start on the outside using a circular and then graduate to
DPNs as you get closer to the center. (I know, I just HAVE to be difficult!)
I just think it would be easier.

I know you must decrease with each round, but by how much? If I start with,
say 100 sts on a circular, is there a formula I should use to know when to
decrease - Knit 2 together every X stitches?

Any insight appreciated!
Abi

I knitted a square from the inside out, for one of the 6x6 exhanges. It
became a star, and no matter how hard I tried doing it from the inside
out, still the four edges would bow in to the center. I then took the
pattern and started at the outside on indeed double pointed needles, I
used 5 I think. The square became nice and flat with straight edges. I
could see right away if it was going to lay flat or not, and added or
decreased the stitches on the four corners. Maybe it would work for a
circle as well. Sample and see if it works. I got my pattern from the
Readers Digest complete guide to needlework

Els

--
hate spam not welcome

Abi i feel with you that starting on the outside is better for ME ,
Try and find a pattern that works regulary from the middle outwards
and do it the other way ,, strat by the maximum end number of stiches
....You might need 2 circulars ,,,i will think about this and see waht
i can work out .
mirjam

Thanks for all the advice, folks!

I was hoping to start from the outside of my disc and work in because my
arthritis somes makes starting a small circumference on DPN difficult. I
have used the two circular method, and may try that, then graduate to DPN
after a few rows, then to circulars as the circle expands.

What I want to avoid is doing a large octagon. I'd like this circle to be,
well, a circle - no points. If I ever master the "perfect circle" I'll post
my findings.

Abi

The Prophet Gallagher known to the wise as , opened the Book of Words, and read unto the people:
I want to knit a flat circle (about 10" across) and not use short rows. I've
looked at a couple of dishcloth and doily patterns and am trying to figure
out the math used to get it flat.

All the ones I've seen have you start in the middle with a few stitches on
DPN. I'd rather start on the outside using a circular and then graduate to
DPNs as you get closer to the center. (I know, I just HAVE to be difficult!)
I just think it would be easier.

I know you must decrease with each round, but by how much? If I start with,
say 100 sts on a circular, is there a formula I should use to know when to
decrease - Knit 2 together every X stitches?

I'm coming to this from the point of view of crochet rather than knit,
but the same assumptions should carry over fine. Working from the
outside in and working from the inside out should (in theory) be
fairly symmetric, since a K2tog working inwards is morally equivalent
to an increase working outwards.

No valeu of X in your above suggested method, however, will work,
since you'll be putting in more decreases in the outer rounds than the
inner rounds. To figure out the right approach, we basically need to
consider what happens as we reduce (or increase) the diameter.

Suppose a stitch has height h and width w, and the work at the moment
has radius r. The circumference of a circle of radius r is 2*pi*r, so
since you want all the stitches in a round to have total length of the
circumference of the round, we need n*w = 2*pi*r (n being the number
of stitches), so n = 2*pi*r/w. Then, on the next round, the radius
will be r+h (if increasing) or r-h (if decreasing), since we've added
some width to the work and changed the radius of the round we're
working on. So this round needs to have 2*pi*(r+h)/w or 2*pi*(r-h)/w
stitches; that is, the number of stitches on this round is more or
less than the previous round by 2*pi*h/w, so that's the number of
increases/decreases you're going to want.

Some notes on this: first, it doesn't depend on r, so you're going to
want the same number of increases/decreases on each round. Also, it
doesn't actually depend on h or w, but rather on the ratio between the
two, so you don't have to laboriously measure a single stitch, but can
instead make a gauge swatch (say, 10 stitches, 10 rows) and measure
the ratio of the height and width of that.

As an example, if your gauge swatch is perfectly square, or slightly
wider than it is tall, then h/w must be 1 or slightly less than 1, so
2*pi*h/w is approximately 6 and you'd want about 6 increases or
decreases per round.

As a final note, the relation C=2*pi*r describes the fact that
ordinary space has zero curvature. Spaces in which C2*pi*r are said
to have _positive curvature_, and in the real world can be considered
as sections of spheres (we use positive-curvature surfaces for the
curve on a hat, for instance); if C2*pi*r then the space has
_negative_ curvature_ and cannot be faithfully embedded in ordinary 3D
space but we try to do so anyways (this corresponds in crochet and
knit to overincreasing, which can cause the edge of the work to be
oddly scalloped or ruffled). The control crochet and knit provide in
adjusting local curvature have been exploited for mathematical
demonstrations, and have been written up on at least two occasions:

David Henderson and Daina Taimina, "Crocheting the Hyperbolic Plane",
Math. Intelligencer, v. 23 (2001), n. 2, 17--28; and

Hinke Osinga and Bernd Krauskopf, "Crocheting the Lorenz Manifold",
Math. Intelligencer, v. 26 (2004), n. 4, 25--37.

--
D. Jacob (Jake) Wildstrom, Math monkey and freelance thinker

"A mathematician is a device for turning coffee into theorems."
-Alfred Renyi

The opinions expressed herein are not necessarily endorsed by the
University of California or math department thereof.

Well, I am humbled! More info than my little brain can process.

At knittersreview.com, I found a bit of more simplified information - "To
knit a circle---any circle for any reason--- all you have to do is have 8
increases/decreases every other row. You can space them anyway you wish as
long as they average 4 per row. For example, 8 every other row, 16 every
fourth row, etc. "

So, once I try it, I'll post my results.

Thanks to all,
Abi

Jake Wildstrom wrote:
The Prophet Gallagher known to the wise as ,
opened the Book of Words, and read unto the people:
I want to knit a flat circle (about 10" across) and not use short
rows. I've looked at a couple of dishcloth and doily patterns and am
trying to figure out the math used to get it flat.

All the ones I've seen have you start in the middle with a few
stitches on DPN. I'd rather start on the outside using a circular
and then graduate to DPNs as you get closer to the center. (I know,
I just HAVE to be difficult!) I just think it would be easier.

I know you must decrease with each round, but by how much? If I
start with, say 100 sts on a circular, is there a formula I should
use to know when to decrease - Knit 2 together every X stitches?

I'm coming to this from the point of view of crochet rather than knit,
but the same assumptions should carry over fine. Working from the
outside in and working from the inside out should (in theory) be
fairly symmetric, since a K2tog working inwards is morally equivalent
to an increase working outwards.

No valeu of X in your above suggested method, however, will work,
since you'll be putting in more decreases in the outer rounds than the
inner rounds. To figure out the right approach, we basically need to
consider what happens as we reduce (or increase) the diameter.

Suppose a stitch has height h and width w, and the work at the moment
has radius r. The circumference of a circle of radius r is 2*pi*r, so
since you want all the stitches in a round to have total length of the
circumference of the round, we need n*w = 2*pi*r (n being the number
of stitches), so n = 2*pi*r/w. Then, on the next round, the radius
will be r+h (if increasing) or r-h (if decreasing), since we've added
some width to the work and changed the radius of the round we're
working on. So this round needs to have 2*pi*(r+h)/w or 2*pi*(r-h)/w
stitches; that is, the number of stitches on this round is more or
less than the previous round by 2*pi*h/w, so that's the number of
increases/decreases you're going to want.

Some notes on this: first, it doesn't depend on r, so you're going to
want the same number of increases/decreases on each round. Also, it
doesn't actually depend on h or w, but rather on the ratio between the
two, so you don't have to laboriously measure a single stitch, but can
instead make a gauge swatch (say, 10 stitches, 10 rows) and measure
the ratio of the height and width of that.

As an example, if your gauge swatch is perfectly square, or slightly
wider than it is tall, then h/w must be 1 or slightly less than 1, so
2*pi*h/w is approximately 6 and you'd want about 6 increases or
decreases per round.

As a final note, the relation C=2*pi*r describes the fact that
ordinary space has zero curvature. Spaces in which C2*pi*r are said
to have _positive curvature_, and in the real world can be considered
as sections of spheres (we use positive-curvature surfaces for the
curve on a hat, for instance); if C2*pi*r then the space has
_negative_ curvature_ and cannot be faithfully embedded in ordinary 3D
space but we try to do so anyways (this corresponds in crochet and
knit to overincreasing, which can cause the edge of the work to be
oddly scalloped or ruffled). The control crochet and knit provide in
adjusting local curvature have been exploited for mathematical
demonstrations, and have been written up on at least two occasions:

David Henderson and Daina Taimina, "Crocheting the Hyperbolic Plane",
Math. Intelligencer, v. 23 (2001), n. 2, 17--28; and

Hinke Osinga and Bernd Krauskopf, "Crocheting the Lorenz Manifold",
Math. Intelligencer, v. 26 (2004), n. 4, 25--37.

Wow!

Katherine

On Fri, 11 Mar 2005 10:02:05 -0500, "Gallagher"
wrote:

Thanks for all the advice, folks!

I was hoping to start from the outside of my disc and work in because my
arthritis somes makes starting a small circumference on DPN difficult. I
have used the two circular method, and may try that, then graduate to DPN
after a few rows, then to circulars as the circle expands.

What I want to avoid is doing a large octagon. I'd like this circle to be,
well, a circle - no points. If I ever master the "perfect circle" I'll post
my findings.

Another thing you can do is crochet the first few rounds, if you know
how to crochet, and then pick up the crochet stitches onto DPNs.
--
Barbara Vaughan

My email address is my first initial followed by my last name at libero dot it.